Volume 13, issue 1 (2013)

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Proof of a stronger version of the AJ Conjecture for torus knots

Anh T Tran

Algebraic & Geometric Topology 13 (2013) 609–624
Abstract

For a knot K in S3, the sl2–colored Jones function JK(n) is a sequence of Laurent polynomials in the variable t that is known to satisfy non-trivial linear recurrence relations. The operator corresponding to the minimal linear recurrence relation is called the recurrence polynomial of K. The AJ Conjecture (see Garoufalidis [Proceedings of the Casson Fest (2004) 291–309]) states that when reducing t = 1, the recurrence polynomial is essentially equal to the A–polynomial of K. In this paper we consider a stronger version of the AJ Conjecture, proposed by Sikora [arxiv:0807.0943], and confirm it for all torus knots.

Keywords
colored Jones polynomial, $A$–polynomial, AJ Conjecture
Mathematical Subject Classification 2010
Primary: 57N10
Secondary: 57M25
References
Publication
Received: 22 November 2011
Accepted: 29 October 2012
Published: 23 March 2013
Authors
Anh T Tran
Department of Mathematics
The Ohio State University
100 Math Tower
231 West 18th Avenue
Columbus OH 43210
USA